Getting Started with Mathematica

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Getting Started with Mathematica
by Hakan Kutucu
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What is Mathematica

• Mathematica is a computer program created by
  Wolfram Research Inc.(1988)
• Mathematica is a powerful desktop computer
  program capable of doing algebraic calculations,
  numerical approximations, and computer graphics.
• It is suitable for both numeric and symbolic
  work, and it has remarkable word-processing
  capabilities as well.

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Some Graphical Examples
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What is Mathematica

• Mathematica has two parts the Kernel and the
  Front End.
• The Kernel is the main part of the system, which
  accepts Mathematica commands, processes them and
  sends back results. This is called evaluating the
  command.
• The Front End is the part of the system that
  handles such things as screen display, printing
  and the creation of Mathematica documents.

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How does Mathematica work?
Mathematica documents are called Notebooks. A
Notebook is a bit like a word-processor document
you can type and edit commands, send them to the
Kernel for evaluation, display the results and
save your work.
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How does Mathematica work?

• You send commands to be evaluated by holding
  down the shift key and pressing the enter key
• Another easy way to evaluate by pressing the
  enter key at the right hand side of keyboard.

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Functionalities of Mathematica

• Numerical Computation
• Equation Solving
• Symbolic calculation
• Calculus
• Graphics
• Self-defined functions
• List
• Pattern Matching
• Animation

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Mathematica Syntax

• Mathematica commands start with a CAPITAL
  letter, e.g. Sinx. If the command is really
  severalwords in English joined together then each
  one starts with a capital but WithNoSpacesInBetwee
  n.
• Case Sensitive the word Fun is different from
  the word fun which is different from the word
  fuN.

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Mathematica Syntax

• Mathematica uses a lot of brackets and all the
  different sorts of them, ( ).
• Arguments of functions are given in square
  brackets .
• Curly brackets, called braces, are used to
  make a list, usually to allow several objects to
  be treated as one.
• Expression are cascaded by () pairs.

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SPECIAL CONSTANTS
Mathematica protects these names they cannot be
used as names for other quantities.
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Arithmetic Operations
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Arithmetic Operations
Order of operation is important . BEDMAS
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N (Numerical)

• (a) Nexpr displays 6 digits by default
• (b) Nexpr, n displays 6 digits when nlt16
• (c) Nexpr, n does not display more digits than
  n originally has.

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Some Mathematical Functions
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Graphics
Mathematica incorporates a wide range of two-and
three-dimensional graphics functions. The
simplest is Plot, which generates two-dimensional
Cartesian graphs
Plotf, x, xmin, xmax generates a plot of f
as a function of x from xmin to xmax. Plotf1,
f2, , x, xmin, xmax plots several
functions fi.
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Graphics (Example)
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Graphics(Options)
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Graphics(Options)
For Other Options the command is OptionsPlot
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3 Dimensional Plotting
Plot3D f, x,xmin,xmax, y,ymin,ymax will
draw the graph of z f(x,y) over the rectangle
xmin,xmaxymin,ymax in the xy-plane.
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3 Dimensional Plotting(Options)
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Three Dimensional Plotting(Options)
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Defining Functions

• A function may return a symbol, a real number, a
  complex matrix, another function....
• Any mathematical object is an acceptable value
  for a function.
• A function may be written using mathematical
  notation, it may be created using programming
  constructs (like for, if/then, etc.), or it could
  even be written in another language entirely
  (Fortran, C, etc.).

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Function Variable Names

• Mathematica variable names can be long, but they
  must not begin with a number,
• Because Mathematica interprets, say, 2dimension
  as 2 dimension.
• Names can end with a number, though x1 is a
  useful way of writing in Mathematica a
  subscripted variable like x1.
• Note also that combinations of letters without
  spaces are interpreted as new variables ax does
  not mean ax.

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Defining Functions
A function can be defined by using the following
form fx_ an expression involving x (no
underbar) Example fx_x23x f4 fa1 ?f
(This shows the definition you made for f. )
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Equation solving

• Use Solve to solve an equation with an exact
  solution, including a symbolic solution.
• Use NSolve or FindRoot to obtain a numerical
  approximation to the solution.
• To use solutions need to use expr/ .x y.

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Matrix Defining

• Entering a matrix
• a1,2,3,4,5,6,7,8,9
• Displays nicely only if told to

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Menus exist but are harder to use than typing
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Matrix Operations
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Matrix Operations (Multiplication)
Matrix multiplication (also called dot or inner
product) is carried out in Mathematica with the
function Dot, typically entered with a dot
short-hand syntax.
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Matrix Operations (Transpose)
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Matrix Operations (Inverse)
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Matrix Operations Exercises

• By using Solve Commabd
• By using The equation Axb